MathDB

In the figure below, area of triangles

AOD, DOC,

and

AOB

is given. Find the area of triangle

OEF

in terms of area of these three triangles.
[asy] import graph; size(11.52cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-2.4,xmax=9.12,ymin=-6.6,ymax=5.16; pair A=(0,0), F=(9,0), B=(4,0), C=(3.5,2), D=(1.94,2.59), O=(2.75,1.57); draw(A--(3,4),linewidth(1.2)); draw((3,4)--F,linewidth(1.2)); draw(A--F,linewidth(1.2)); draw((3,4)--B,linewidth(1.2)); draw(A--C,linewidth(1.2)); draw(B--D,linewidth(1.2)); draw((3,4)--O,linewidth(1.2)); draw(C--F,linewidth(1.2)); draw(F--O,linewidth(1.2)); dot(A,ds); label("

A

",(-0.28,-0.23),NE*lsf); dot(F,ds); label("

F

",(8.79,-0.4),NE*lsf); dot((3,4),ds); label("

E

",(3.05,4.08),NE*lsf); dot(B,ds); label("

B

",(4.05,0.09),NE*lsf); dot(C,ds); label("

C

",(3.55,2.08),NE*lsf); dot(D,ds); label("

D

",(1.76,2.71),NE*lsf); dot(O,ds); label("

O

",(2.57,1.17),NE*lsf); clip((xmin,ymin)--(xmin,ymax)--(xmax,ymax)--(xmax,ymin)--cycle); [/asy]

Problem Statement